SPM 2021 Add Maths Paper 1, Question 12Probability Distribution

Solved on video in English and Bahasa Melayu · Form 5, Probability Distribution · 4:52 video

The question

(a)

A random variable X has a binomial distribution with 5 trials such that the probability of success in each trial is p and the probability of failure is q. Table 1 shows parts of the probability distribution of X: the entry 81/128 spans X = 0 and X = 1 (so P(X = 0) + P(X = 1) = 81/128), and the entry 1/64 spans X = 4 and X = 5 (so P(X = 4) + P(X = 5) = 1/64). State the value of P(X = 2) + P(X = 3) in fraction form.

(b)

Hence, show that p = 3/(16q). (X is binomial with n = 5 trials, success probability p, failure probability q, and P(X = 2) + P(X = 3) = 45/128 from part (a).)

SPM 2021 Add Maths Paper 1, Question 12: the question as drawn in Eduly's video4:52

Part (a)

Step 1

The total probability of all outcomes equals 1.

Why this step

Every outcome is covered, so all six probabilities add to 1. Many students miss this and try the nCr formula instead, then get stuck.

4 more steps, each with the reason for it, in the full solution

Final answer

P(X = 2) + P(X = 3) = 45/128

Where students lose marks

Watch out: all probabilities add to 1, so subtract the known pairs from 1 instead of expanding each term with nCr.

Part (b)

6 more steps, each with the reason for it, in the full solution

Final answer

Shown

Where students lose marks

Watch out: 'hence' means use the 45/128 from part (a). Don't start again from scratch.

Watch every step of this question solved on video (4:52), with the reason behind each step and a box that checks your own answer.

Start 7 days freeAlready a member? Watch it now

No card. Every past-year question on video, in English and BM.

All questions in SPM 2021 Paper 1

Probability Distribution: lessons and every past-year question

Baca dalam Bahasa Melayu

More Probability Distribution questions

Questions are re-typeset by Eduly for study and commentary. Eduly is not affiliated with Lembaga Peperiksaan Malaysia or the Ministry of Education.